Trajectory and force control of a manipulator with elastic links

This paper deals with trajectory and force control of a two-link manipulator with elastic links. The manipulator has a macro-micro mechanism and at the tip of which is an end-effector with a force sensor. Equations of motion are first derived by using a finite-element method for the elastic deformations. Then, by eliminating the residual modes based on the eigenvalue analysis, the reduced-order equations for controller design are derived. Geometrical constraints are modeled by using a Lagrangian multiplier. The proposed control system consists of a feedforward controller and a feedback controller. The feedforward controller generates the input torques and force based on inverse dynamics. It also generates the reference signals for the feedback controller based on inverse kinematics. The calculation methods for inverse dynamics and inverse kinematics are based on the algorithm that we have proposed. The performance of the proposed control system is verified by numerical simulations and hardware experiments.